How to Use GAUSS Function in Google Sheets

The GAUSS function in Google Sheets is useful when you need to calculate the probability that a random variable drawn from a normal distribution will be between z standard deviations above or below the mean.

The function receives its name from the Gaussian distribution, which is another name for the normal distribution. It is characterized by its bell-curved shape.

The rules for using the GAUSS function in Google Sheets are as follows:

  • The function requires only one argument z. Z indicates the number of standard deviations from the mean.
  • The function then outputs the probability that a random variable falls between the mean and z.

Let’s take a look at one use case where we can use the GAUSS function.

In this example, let’s say we would like to know the probability of a random male to have a height 1 standard deviation away from the mean. We know that height follows a normal distribution. Let’s say that the average height of the population is 180cm with a standard deviation of about 6cm. How likely is it that a random person will be a single standard deviation above or below the mean? How likely is it for a person to be two standard deviations below the mean?

With the GAUSS function, it’s quite simple to perform these calculations.

This use case is just one way to use the GAUSS function in Google Sheets. We can use the GAUSS function to return the probability of any value falling under a particular range in a normal distribution. Besides height, you can find normal distribution in things like IQ scores, shoe sizes, and blood pressure levels.

Now that we have an idea of when to use the GAUSS function in Google Sheets, let’s figure out how to write the function ourselves.

 

 

The Anatomy of the GAUSS Function

The syntax of the GAUSS function is as follows:

=GAUSS(z)

Let’s look at each term to understand what they mean.

  • = the equal sign is how we start any function in Google Sheets.
  • GAUSS() is our GAUSS function. It returns the probability that a random value will fall between the mean and z standard deviations from the mean
  • z refers to how far away from the mean a random variable might be
  • If the z argument is negative, GAUSS(z) will return a negative result.

 

 

A Real Example of Using GAUSS Function

Let’s look at a real example of the GAUSS function being used in a Google Sheets spreadsheet.

In the table below, we can see how we can use the GAUSS function to generate the precise probability for a specific range in the normal distribution. For example, there is a 34.13% probability that a variable in a normal distribution would fall between the mean and 1 standard deviation above the mean. 

Given the values stated earlier regarding height, that means that we can expect 34.14% of people in a population to fall between 180cm and 186cm. Similarly, we know that 99.7% of people fall between 162cm and 198cm (mean plus and minus three standard deviations).
Using the GAUSS Function in Google Sheets to find probabilities

 

You can generate your own copy of the spreadsheet above using the link attached below. 

If you’re ready to try out the GAUSS function in Google Sheets, let’s begin writing it ourselves!

 

 

How to Use GAUSS Function in Google Sheets

In this section, we will go through each step needed to start working with the GAUSS function in Google Sheets. 

Follow these five quick steps to start using the GAUSS function:

  1. First, let’s select the cell which will hold the result of our GAUSS function.
    selecting the cell to place our GAUSS Function in Google Sheets

  2. Next, we just simply type the equal sign ‘=‘ to begin the function, followed by ‘GAUSS(‘. 
  3. You may find a tooltip box with hints on how to use the GAUSS function. We can click on the arrow on the top-right-hand corner of the box to minimize it if necessary.
    typing GAUSS function into the formula bar

  4. The next step is to type in our value for standard deviations. In this case, the value is in column A in cell A2. Afterward, simply hit Enter on your keyboard to let the function evaluate.
    Returning the probability that a value will fall within half a standard deviation above the mean

  5. If you need to include both a standard deviation below and above the mean, simply multiply the result by two.
    Doubling the result of gauss will cover both above and below the mean

 

 

Frequently Asked Questions (FAQ)

  1. Why does my COUNTA formula return a #VALUE! error?
    Make sure that the argument is a valid number. If the z argument is not a valid data type, GAUSS returns the #VALUE! error value. 
  2. What happens if you reference a cell without any data?
    When z references a value in another cell in your worksheet (e.g., “GAUSS(C2)”), the GAUSS function will return a 0 if there are no data in the cell.

That’s all you need to know to start using the GAUSS function in Google Sheets. Hopefully, this step-by-step guide shows how quickly you can find the probability for a certain value to fall under a range in a normal distribution. 

The GAUSS function is just one example of a statistical function in Google Sheets. With so many other Google Sheets functions out there, you can surely find one that suits your needs.

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